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Simplifying 3h2 + 12h + -4891 = 0 Reorder the terms: -4891 + 12h + 3h2 = 0 Solving -4891 + 12h + 3h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1630.333333 + 4h + h2 = 0 Move the constant term to the right: Add '1630.333333' to each side of the equation. -1630.333333 + 4h + 1630.333333 + h2 = 0 + 1630.333333 Reorder the terms: -1630.333333 + 1630.333333 + 4h + h2 = 0 + 1630.333333 Combine like terms: -1630.333333 + 1630.333333 = 0.000000 0.000000 + 4h + h2 = 0 + 1630.333333 4h + h2 = 0 + 1630.333333 Combine like terms: 0 + 1630.333333 = 1630.333333 4h + h2 = 1630.333333 The h term is 4h. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4h + 4 + h2 = 1630.333333 + 4 Reorder the terms: 4 + 4h + h2 = 1630.333333 + 4 Combine like terms: 1630.333333 + 4 = 1634.333333 4 + 4h + h2 = 1634.333333 Factor a perfect square on the left side: (h + 2)(h + 2) = 1634.333333 Calculate the square root of the right side: 40.426888738 Break this problem into two subproblems by setting (h + 2) equal to 40.426888738 and -40.426888738.Subproblem 1
h + 2 = 40.426888738 Simplifying h + 2 = 40.426888738 Reorder the terms: 2 + h = 40.426888738 Solving 2 + h = 40.426888738 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = 40.426888738 + -2 Combine like terms: 2 + -2 = 0 0 + h = 40.426888738 + -2 h = 40.426888738 + -2 Combine like terms: 40.426888738 + -2 = 38.426888738 h = 38.426888738 Simplifying h = 38.426888738Subproblem 2
h + 2 = -40.426888738 Simplifying h + 2 = -40.426888738 Reorder the terms: 2 + h = -40.426888738 Solving 2 + h = -40.426888738 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = -40.426888738 + -2 Combine like terms: 2 + -2 = 0 0 + h = -40.426888738 + -2 h = -40.426888738 + -2 Combine like terms: -40.426888738 + -2 = -42.426888738 h = -42.426888738 Simplifying h = -42.426888738Solution
The solution to the problem is based on the solutions from the subproblems. h = {38.426888738, -42.426888738}
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